Like Fractions And Unlike Fractions
A fraction is a number that represents a portion of an entire object or a group of objects. It is determined by two numbers, one at the top and one at the bottom of the fraction bar, called the numerator and denominator respectively. Depending on the similarity of the denominator, we classify two or more fractions into like fractions and unlike fractions. They are also sometimes called similar and different fractions. The meaning of like is the same and not the same means different. Now, in this article, we will learn how to perform arithmetic operations on both types of fractions along with how to convert fractions that do not look like fractions into fractions that are similar to the examples. Let us learn more here. Read: what are analog fractionsAlso, read:
Like fractions
Contents
Groups of two or more fractions with the same denominator are called like fractions. Or we can say that fractions with the same number in the denominator are called fractions. For example, 1/7, 2/7, 5/7, 6/7 are all like fractions, whose denominator is 7.Can easily perform arithmetic operations such as addition and subtraction as fractions. We do not need to neutralize the denominators while performing both operations. Let us understand with the help of examples.
Addition and subtraction of fractions like
When we add or subtract similar fractions, the denominator stays the same and only the numerators are added or subtracted respectively. Here are examples.Example 1: Add 2/3 and 5/3Solution: 2/3 + 5/3 = (2 + 5) / 3 = 7/3Example 2: Subtract 1/2 by 11/2.Solution: 11/2 – 1/2 = (11-1) / 2 = 10/2 = 5
Points to remember
- 2/4, 4/8, 1/2, etc. are not the same as fractions, although when simplified they all result in 1/2.
- 6/16 and 6/26 are not the same as fractions. The numerators are the same, but the denominators are not.
- 2, 3, 4 are like fractions because their denominator is considered to be 1, which means that these fractions are 2/1, 3/1, and 4/1.
Not like fractions
Fractions with different denominators are called not like fractions. Here the denominators of the fractions have different values. For example, 2/3, 4/9, 6/67, 9/89 are not the same as fractions, because the denominators here are different, so it is not easy to add or subtract such fractions. To perform arithmetic operations like addition and subtraction, we must first convert the dissimilar fractions into the same fraction. Then we perform the necessary operations.
The addition and subtraction of fractions is not the same as
When we add and subtract two fractions that are not the same, we have to make the denominators equal first and then do the corresponding math. There are two methods by which we can make the denominator equal. They are:
- Cross-multiplication method
- LCM . method
Read more: What happened to mary jane on masterchef cross multiplication method, we cross multiply the numerator of the first fraction by the denominator of the second. Then multiply the numerator of the second fraction by the denominator of the first fraction. Now multiply both denominators and take it as the common denominator. Then we can add or subtract fractions now.Example: Add 1/3 and 3/4Solution: 1/3 + 3/4 By cross multiplication, we get; =[(1 x 4) + (3 x 3)]/ 3 x 4 = (4 + 9) / 12 = 13/12 In LCM . method, we need to get the LCM of the denominators of the given fractions first. Now using this LCM make all fractions like fractions. Then we can simplify the numerator.Example: Add 3/8 and 5/12Solution: 3/8 + 5/12 Now take the LCM of 8 and 12, we get; LCM(8, 12) = 2 x 2 x 2 x 3 = 24Now multiply the given fractions to get the denominator by 24, such that ; =[(3 x 3)/(8 x 3)] + [(5 x 2) + (12 x 2)]= (24/9) + (24/10) Read more: EaseUS MobiSaver | Top Q&A = (9 + 10) / 24 = 19/24.
Convert Dislike Fractions to Like Fractions
Like fractions facilitate the comparison of fractions. So, it is often necessary to convert fractions that don’t look like them to them, let’s convert 1, 4/5, 7/10 and 1/2 into fractions like that. Conversion steps:
- Find the GCC of the denominators. The LCM of 1, 5, 10 and 2 is 10.
- Calculate their equivalent fractions with the same denominator, i.e. LCM.
1/1 = (1 × 10) / (1 × 10) = 10/104/5 = (4 × 2) / (5 × 2) = 8/107/10 = (7 × 1) / (10 × 1 ) = 7/101/2 = (1 × 5) / (2 × 5) = 5/101, 4/5, 7/10 and 1/2 which unlike fractions, can be represented as 10/ 10.8 / 10, 7/10 and 5/10 are like fractions, it should be noted that when the denominators are equal then the fractions can be compared with each other. You will not be able to answer the largest of 1, 4/5, 7/10 and 1/2. But once they have been converted to 10/10, 8/10, 7/10 and 5/10, you can sort them in ascending order of 5/10, 7/10, 8/10 and 10/10 very convenient.
Types of fractions
There are mainly three types of fractions, they are:
- The appropriate part
- Fraction is not correct
- Mixed fractions
Correct and incorrect fractions
Similar to fractions like and unlike fractions, we have another type of fraction, called true and false fractions.
- One appropriate part is a fraction with a value less than 1. Or we can say, when the value of the numerator is less than the denominator, then such fractions are called appropriate fractions — for example, 1/2, 1/3, 4/5, 6/7, 8/9, etc
- One incorrect fraction is a fraction with a value greater than 1. When the value of the numerator is greater than the value of the denominator, the fraction is said to be incorrect. For example, 3/2, 5/4, 4/3. 8/3, etc
Mixed fractions
When a number is the union of an integer and an appropriate fraction, it is called a mixed fraction. For example:
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